Exercise 3.5 1. Let A=(} 1&2 4&3 ) Then determine each of the following. a. 4A b. -(1)/(3)B c. 2A+3B d. matrix C such that A+2C=B e A-(1)/(2)B f. 3A-2B 2. Let A = A=(} 0&1&2 1&-1&4 5&1&6 ) Then find a. 3A b. -(1)/(2)B c. 3A+2B d. matrix C such that A-2C=B e. A-5B f. 3A-2B 3. Let A=(} 1&-2&3 0&-5&2 )

1. <br />a. $4A = \begin{pmatrix} 4 & 8 \\ 16 & 12 \end{pmatrix}$<br />b. $-\frac{1}{3}B = \begin{pmatrix} -1 & \frac{1}{3} \\ -\frac{2}{3} & \frac{4}{3} \end{pmatrix}$<br />c. $2A + 3B = \begin{pmatrix} 11 & 1 \\ 10 & -6 \end{pmatrix}$<br />d. $A + 2C = B \Rightarrow 2C = B - A \Rightarrow C = \frac{1}{2} \begin{pmatrix} 2 & -1 \\ 2 & -3 \end{pmatrix}$<br />e. $A - \frac{1}{2}B = \begin{pmatrix} \frac{1}{2} & \frac{5}{2} \\ \frac{14}{2} & \frac{7}{2} \end{pmatrix}$<br />f. $3A - 2B = \begin{pmatrix} 3 & 8 \\ 6 & 11 \end{pmatrix}$<br /><br />2. <br />a. $3A = \begin{pmatrix} 0 & 3 & 6 \\ 3 & -3 & 12 \\ 15 & 3 & 18 \end{pmatrix}$<br />b. $-\frac{1}{2}B = \begin{pmatrix} -\frac{1}{2} & 0 & -\frac{1}{2} \\ -\frac{1}{2} & 0 & 0 \\ 0 & 0 & -1 \end{pmatrix}$<br />c. $3A + 2B = \begin{pmatrix} 1 & 3 & 5 \\ 4 & -3 & 12 \\ 17 & 3 & 18 \end{pmatrix}$<br />d. $A - 2C = B \Rightarrow 2C = A - B \Rightarrow C = \frac{1}{2} \begin{pmatrix} -1 & 1 & -1 \\ 0 & -1 & 2 \\ -5 & -1 & 4 \end{pmatrix}$<br />e. $A - 5B = \begin{pmatrix} -1 & 1 & -1 \\ 0 & -1 & 4 \\ -5 & 1 & 4 \end{pmatrix}$<br />f. $3A - 2B = \begin{pmatrix} -1 & 3 & 5 \\ 2 & -3 & 12 \\ 13 & 3 & 16 \end{pmatrix}$<br /><br />3. <br />a. $2A = \begin{pmatrix} 2 & -4 & 6 \\ 0 & -10 & 4 \end{pmatrix}$<br />b. $3B = \begin{pmatrix} -9 & 6 & 3 \\ 12 & 0 & -6 \end{pmatrix}$<br />c. $2C = \begin{pmatrix} 4 & 4 & 0 \\ 16 & 0 & -12 \end{pmatrix}$<br />d. $A + B + C = \begin{pmatrix} 0 & 2 & 10 \\ 12 & -10 & -4 \end{pmatrix}$<br />e. $A - B + C = \begin{pmatrix} 4 & -6 & 8 \\ 12 & -10 & -4 \end{pmatrix}$<br />f. $A + 2B - 3C = \begin{pmatrix} -11 & 16 & -18 \\ 4 & -10 & 10 \end{pmatrix}$